# Multi-UAV Optimal Mission Assignment and Path Planning for Disaster Rescue Using Adaptive Genetic Algorithm and Improved Artificial Bee Colony Method

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

## 3. Optimization Modelling and Its Solution

#### 3.1. The Proposed Computational Flow Chart

#### 3.2. The Threat Source Modelling Methods

- (1)
- The severe weather threat source

_{WR}will be high (P

_{WR}= 1); and if no rain appears in that zone, the threat degree would be higher with the increment of wind speed.

_{i,j,p,WR}represents the threat degree of rain and wind, i means the i

^{th}UAV, j means the j

^{th}threat source, p is the p

^{th}iteration number, WR indicates the wind and rain threat sources; P

_{i,j,p,R}and P

_{i,j,p,W}are the threat degrees of rain and wind, respectively; d

_{WR}is the distance between the UAV and weather threat source center; D

_{WR}is the radius of weather threat source; symbols “||” and “&” represent the relationship operators “or” and “and” between two variables; P

_{i,p,WR}is the integrated severe weather threat degree of the i

^{th}UAV; and M

_{1}is the total amount of weather threat source (weather station).

- (2)
- The transmission tower threat source

_{i,j,p,q}(x, y) (q = 1, 2) is the probability density function of bi-GMM function, i means the i

^{th}UAV, j is of the j

^{th}threat source (transmission tower), p is the p

^{th}iteration number, q is the number of Gaussian function; μ1

_{i,j,p,q}and μ2

_{i,j,p,q}are the means, σ1

_{i,j,p,q}and σ2

_{i,j,p,q}are the variances, ρ

_{i,j,p,q}is the correlation coefficient; P

_{i,j,p,TT}is the security threat degree of the j

^{th}transmission tower; w

_{j,p,q}is the weight of two Gaussian functions; TT means the transmission tower threat source; P

_{i,p,TT}is the integrated transmission tower threat degree of the i

^{th}UAV; M

_{2}is the total number of transmission tower in the investigated area.

- (3)
- The upland threat source

_{i,j,p}, $\overline{{A}_{i,j,p}{O}_{i,j,p,m}}$, $\overline{{C}_{i,j,p}{O}_{i,j,p,m}}$, $\overline{{B}_{i,j,p}{O}_{i,j,p,t}}$, $\overline{{O}_{i,j,p,t}{O}_{i,j,p,m}}$, $\overline{{E}_{i,j,p}{F}_{i,j,p}}$, $\overline{{G}_{i,j,p}{H}_{i,j,p}}$, $\overline{{C}_{i,j,p}{D}_{i,j,p}}$ are defined in Figure 5; i means the i

^{th}UAV, j is the j

^{th}upland threat source, p is the p

^{th}iteration number, m means the circle center of the circular cone in bottom; t is the circle center of circular cone in middle; “||” and “&” represent the relationship operators of “or” and “and” between two variables; P

_{i,j,p,UT}represents the threat source of the j

^{th}upland; UT means the upland threat source; P

_{i,p,UT}is the integrated upland threat effect of the i

^{th}UAV; M

_{3}is the total number of upland in the disaster zone.

#### 3.3. The Cost-Revenue Function

_{i,p}

_{,Total}is the total cost and revenue in the p

^{th}iteration computation of the i

^{th}UAV; C

_{i,p}

_{,MP}is the cost function of the mission point; C

_{i}

_{,p,RP}is the cost function of the recovery point; ${\delta}_{MP}^{D}$, ${\delta}_{MP}^{O}$, ${\delta}_{MP}^{WR}$, ${\delta}_{MP}^{TT}$, ${\delta}_{MP}^{UT}$ are the weights of distance factor, oil consumption factor, weather threat factor, transmission tower threat factor, and upland threat factor, respectively; K is the total number of mission points; similarly, ${\delta}_{RP}^{D}$, ${\delta}_{RP}^{O}$, ${\delta}_{RP}^{WR}$, ${\delta}_{RP}^{TT}$, and ${\delta}_{RP}^{UT}$ are the corresponding weights of recovery point; P

_{i,p,D}(k), P

_{i,p,O}(k), P

_{i,p,WR}(k), P

_{i,p,TT}(k), and P

_{i,p,UT}(k) are the cost values of distance factor, oil consumption factor, costs of weather threat factor, transmission tower factor, and upland threat factor of the mission point k; and P

_{i,p,D}(c), P

_{i,p,O}(c) P

_{i,p,WR}(c), P

_{i,p,TT}(c), and P

_{i,p,UT}(c) are the corresponding cost values in recovery point; r

_{p}, s

_{p}, and t

_{p}are the amounts of drug delivery UAV, image collection UAV, and communication relay UAV in the p

^{th}iteration, respectively; α is the parameter of drug delivery UAV which means the rate of a successful drug delivery; β is the parameter of image collection UAV which indicates the improvement probability of a drug delivery; γ is the parameter of communication relay UAV which presents the decreasing probability of all kinds of threat degrees; R(k) is the revenue of the k

^{th}mission point; ω

_{1}and ω

_{2}are weights, ω

_{1}= 1.0 and ω

_{2}= 10.0; I is the total number of UAVs.

#### 3.4. The Optimal Computational Methods: AGA and IABC

- (1)
- The optimal mission assignment of multiple mission points using AGAThe multi-UAV can be allocated into different UAV groups by AGA to accomplish the rescue task. The computational steps of AGA are listed below.
- (a)
- The population initialization. The initial population is generated, i.e., a series of initial solutions of mission assignment are created by the random number. The population size N_AGA, the current iteration number p_AGA, the maximum iteration number p_AGA
_{max}, the crossing probability P_{p_AGA,C}, and the mutation probability P_{p_AGA,M}etc., are set. - (b)
- The fitness function calculation [44]. The calculation method of the fitness function is shown by Equation (16).$${f}_{p\_AGA}=T{2}_{p\_AGA}$$
_{p_AGA}is the fitness function in the p_AGA^{th}iteration; T2_{p_AGA}is defined in (15). - (c)
- The iterative computation of AGA. Three kinds of computations are implemented [45]: the selection operation, crossover operation, and mutation operation. First, the selection operation considers the estimation result of fitness function, and its probability is defined in Equation (17). The roulette wheel selection method is utilized in this study. Second, the crossover processing is carried out by exchanging several gene fragments at the positions of two randomly selected individuals. Third, the mutation step is achieved by switching two genes of one randomly selected individual. The probabilities of crossover and mutation operations are defined in (18) and (19).$${P}_{p\_AGA,S}=\frac{{f}_{p\_AGA}}{{\displaystyle \sum _{p\_AGA=1}^{N\_AGA}{f}_{p\_AGA}}}$$$${P}_{p\_AGA,C}=\{\begin{array}{cc}{a}_{p\_AGA}\times \frac{{P}_{p\_AGA,C\_\mathrm{max}}({f}_{p\_AGA,\mathrm{max}}-{f}_{p\_AGA})}{{f}_{p\_AGA,\mathrm{max}}-{f}_{p\_AGA,mean}}& {f}_{p\_AGA}\ge {f}_{p\_AGA,mean}\\ {b}_{p\_AGA}\times {P}_{p\_AGA,C\_\mathrm{max}}& {f}_{p\_AGA}<{f}_{p\_AGA,mean}\end{array}$$$${P}_{p\_AGA,M}=\{\begin{array}{cc}{c}_{p\_AGA}\times \frac{{P}_{p\_AGA,M\_\mathrm{max}}({f}_{p\_AGA,\mathrm{max}}-{f}_{p\_AGA})}{{f}_{p\_AGA,\mathrm{max}}-{f}_{p\_AGA,mean}}& {f}_{p\_AGA}\ge {f}_{p\_AGA,mean}\\ {d}_{p\_AGA}\times {P}_{p\_AGA,M\_\mathrm{max}}& {f}_{p\_AGA}<{f}_{p\_AGA,mean}\end{array}$$
_{p_AGA}_{,S}is the selection probability; f_{p_AGA}is the fitness function in the p_AGA^{th}iteration; N_AGA is the maximum population number; P_{p_AGA}_{,C}is the cross probability; a_{p_AGA}, b_{p_AGA}, c_{p_AGA}, and d_{p_AGA}are the control parameters in the p_AGA^{th}iteration, a_{p_AGA}= 1.0, b_{p_AGA}= 1.2, c_{p_AGA}= 1.0, and d_{p_AGA}= 1.35 in this study; P_{p_AGA}_{,C_max}is the maximum of cross probability; f_{p_AGA}_{,max}is the maximum of fitness function; f_{p_AGA}_{,mean}is the mean of fitness function; P_{p_AGA}_{,M}is the mutation probability; P_{p_AGA}_{,M_max}is the maximum of mutation probability.

_{AGA}is an adjustment parameter; h

_{i}is a variable; $T{2}_{p\_AGA}^{\mathrm{max}}$ is the maximum of cost-revenue function; p_AGA

_{max}is the maximum iteration number.

- (2)
- The optimal path planning between neighboring mission points using IABCAn IABC algorithm is used to find the optimal path between neighboring mission points. The basic computational steps of artificial bee colony (ABC) algorithm are presented below.
- (a)
- The population initialization. The random solutions of ABC algorithm are created. The corresponding computation method [47] can be written by (23). The maximum iteration is also set, and the initial iteration number is 0.$${x}_{ij}={x}_{j}^{\mathrm{min}}+rand(-1,1)\left({x}_{j}^{\mathrm{max}}-{x}_{j}^{\mathrm{min}}\right)$$
_{ij}is the coordinate of flight path; x_{j}^{min}and x_{j}^{max}are the minimum and maximum values of x_{ij}; i = 1, 2, …, NP, and NP is the total number of bees; j = 1, 2, …, D. Here D is the dimension of estimated parameter, D = 2 in this study. - (b)
- The path updating of employed foragers. First, the solutions v
_{ij}of employed foragers can be computed by (24), and then the fitness function will be estimated. Here, the fitness function uses the cost-revenue function in Equation (14) to estimate its fitness degree by Equation (25). The classical greedy algorithm [48] is used to select the proper solution. Second, the probability P_{p_IABC}is calculated by (26) and the corresponding scouter can be selected properly. Third, the solution v_{ij}of the onlooker from the solutions x_{ij}selected depending on P_{p_IABC}will also be computed by (24); and the greedy algorithm will be used again to select the proper solution. Fourth, the abandoned solution of scouter will be determined, and a new randomly solution will be considered for them. Fifth, the best solution will be recorded in this round and the iteration counter will be added by 1.$${v}_{ij}={x}_{ij}+rand(-1,1)\left({x}_{ij}-{x}_{kj}\right)$$$${f}_{p\_IABC}=\{\begin{array}{cc}\frac{1}{1+T{1}_{p\_IABC}}\hfill & T{1}_{p\_IABC}\ge 0\\ 1+\left|T{1}_{p\_IABC}\right|\hfill & else\end{array}$$$${P}_{p\_IABC}=\frac{{f}_{p\_IABC}}{{\displaystyle \sum _{p\_IABC=1}^{NP}{f}_{p\_IABC}}}$$_{p_IABC}is the fitness function of solution which is proportional to the nectar amount; T1_{p_IABC}is the cost-revenue function of the p_IABC^{th}iteration. - (c)
- The iteration computation will be terminated if the iteration counter reach its upper limitation.

_{best}

_{,j}will avoid the local minimum solution, fasten convergence speed, and keep algorithm to hold the global searching ability to some extent. In that stage, the convergence speed still can high.

_{best}

_{,j}is the j

^{th}dimension component of global optimal solution of current population; ε(p_IABC) and δ(p_IABC) are the balanced searching factors, p_IABC is the current iteration number, p_IABC

_{max}is the maximum iteration number.

## 4. Results and Discussions

#### 4.1. The Evaluation Experiment of AGA

#### 4.2. The Evaluation Experiment of IABC

#### 4.3. The Evaluation Experiment of Disaster Rescue Simulation

#### 4.4. Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ABC | Artificial bee colony |

AGA | Adaptive Genetic algorithm |

AHP | Analytic hierarchy process |

APFA | Artificial potential field algorithm |

GA | Genetic algorithm |

GMM | Gaussian mixed model |

IABC | Improved artificial bee colony |

LES | Large Eddy Simulations |

PC | Personal computer |

PSO | Particle swarm optimization |

UAV | Unmanned aerial vehicle |

WRF | Weather research and forecasting |

## Nomenclature

${P}_{i,j,p,WR}$ | The threat degree of rain and wind of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation. |

${P}_{i,j,p,R}$ | The threat degree of rain of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation. |

${P}_{i,j,p,W}$ | The threat degree of wind of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation. |

${d}_{WR}$ | The distance between UAV and weather threat source center. |

${D}_{WR}$ | The radius of weather threat source. |

${P}_{i,p,WR}$ | The integrated weather threat degree of the i^{th} UAV under the p^{th} iterative computation. |

${M}_{1}$ | The total amount of weather threat source. |

${f}_{i,j,p,q}(x,y)$ | The probability density function of bi-GMM function of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

$\mu {1}_{i,j,p,q}$ | The mean of Gaussian function 1 of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

$\mu {2}_{i,j,p,q}$ | The mean of Gaussian function 2 of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

$\sigma {1}_{i,j,p,q}$ | The variance of Gaussian function 1 of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

$\sigma {2}_{i,j,p,q}$ | The variance of Gaussian function 2 of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

${\rho}_{i,j,p,q}$ | The correlation coefficient of bi-GMM of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation, q is the number of Gaussian function. |

${P}_{i,j,p,TT}$ | The threat degree of transmission tower of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation. |

${\omega}_{j,p,q}$ | The weight of Gaussian function, j is the number of threat source, p is number of iteration times, q is the number of Gaussian function. |

${P}_{i,p,TT}$ | The integrated transmission tower threat degree of the i^{th} UAV in the p^{th} threat source. |

${M}_{2}$ | The total number of transmission tower in the investigated area. |

${\theta}_{i,j,p}$ | Please see the definition in Figure 5. |

$\overline{{A}_{i,j,p}{O}_{i,j,p,m}}$ | Please see the definition in Figure 5. |

$\overline{{C}_{i,j,p}{O}_{i,j,p,m}}$ | Please see the definition in Figure 5. |

$\overline{{B}_{i,j,p}{O}_{i,j,p,t}}$ | Please see the definition in Figure 5. |

$\overline{{O}_{i,j,p,t}{O}_{i,j,p,m}}$ | Please see the definition in Figure 5. |

$\overline{{E}_{i,j,p}{F}_{i,j,p}}$ | Please see the definition in Figure 5. |

$\overline{{G}_{i,j,p}{H}_{i,j,p}}$ | Please see the definition in Figure 5. |

$\overline{{C}_{i,j,p}{D}_{i,j,p}}$ | Please see the definition in Figure 5. |

${P}_{i,j,p,UT}$ | The threat degree of upland of the i^{th} UAV in the j^{th} threat source under the p^{th} iterative computation. |

${P}_{i,p,UT}$ | The integrated threat degree of upland of the i^{th} UAV under the p^{th} iterative computation. |

${C}_{i,p,Total}$ | The total cost and revenue of the i^{th} UAV in the p^{th} iterative computation. |

${C}_{i,p,MP}$ | The mission point cost function of the i^{th} UAV under the p^{th} iterative computation. |

${C}_{i,p,RP}$ | The recovery point cost function of the i^{th} UAV under the p^{th} iterative computation. |

${\delta}_{MP}^{D}$ | The weight of distance factor of mission point. |

${\delta}_{MP}^{O}$ | The weight of oil consumption factor of mission point. |

${\delta}_{MP}^{WR}$ | The weight of weather threat factor of mission point. |

${\delta}_{MP}^{TT}$ | The weight of transmission tower threat factor of mission point. |

${\delta}_{MP}^{UT}$ | The weight of upland threat factor of mission point. |

$K$ | The total number of mission point. |

${\delta}_{RP}^{D}$ | The weight of distance factor of recovery point. |

${\delta}_{RP}^{O}$ | The weight of oil consumption factor of recovery point. |

${\delta}_{RP}^{WR}$ | The weight of weather threat factor of recovery point. |

${\delta}_{RP}^{TT}$ | The weight of transmission tower threat factor of recovery point. |

${\delta}_{RP}^{UT}$ | The weight of upland threat factor of recovery point. |

${P}_{i,p,D}(k)$ | The distance cost value of mission point k of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,O}(k)$ | The oil consumption cost value of mission point k of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,WR}(k)$ | The weather cost value of mission point k of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,TT}(k)$ | The transmission tower cost value of mission point k of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,UT}(k)$ | The upland cost value of mission point k of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,D}(c)$ | The distance cost value of recovery point c of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,O}(c)$ | The oil consumption cost value of recovery point c of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,WR}(c)$ | The weather cost value of recovery point c of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,TT}(c)$ | The transmission tower cost value of recovery point c of the i^{th} UAV under the p^{th} iterative computation. |

${P}_{i,p,UT}(c)$ | The upland cost value of recovery point c of the i^{th} UAV under the p^{th} iterative computation. |

${r}_{p}$ | The amount of drug delivery UAV under the p^{th} iterative computation. |

${s}_{p}$ | The amount of image collection UAV under the p^{th} iterative computation. |

${t}_{p}$ | The amount of communication relay UAV under the p^{th} iterative computation. |

$\alpha $ | The rate of successful drug delivery of drug delivery UAV. |

$\beta $ | The improvement probability of drug delivery caused by image collection UAV. |

$\gamma $ | The decreasing probability of threat source caused by communication relay UAV. |

$R(k)$ | The revenue of the k^{th} mission point. |

${\omega}_{1}$ | The weight of Gaussian function 1. |

${\omega}_{2}$ | The weight of Gaussian function 2. |

$I$ | The total amount of UAV. |

${f}_{p\_AGA}$ | The fitness function of AGA under the p_AGA^{th} iteration. |

$T{2}_{p\_AGA}$ | The AGA application of Equation (15). |

${P}_{p\_AGA,S}$ | The selection probability of AGA under the p_AGA^{th} iteration. |

$N\_AGA$ | The maximum population amount of AGA. |

${P}_{p\_AGA,C}$ | The cross probability of AGA under the p_AGA^{th} iteration. |

${a}_{p\_AGA}$ | A control parameter of AGA fitness function under the p_AGA^{th} iteration. |

${b}_{p\_AGA}$ | A control parameter of AGA fitness function under the p_AGA^{th} iteration. |

${c}_{p\_AGA}$ | A control parameter of AGA fitness function under the p_AGA^{th} iteration. |

${d}_{p\_AGA}$ | A control parameter of AGA fitness function under the p_AGA^{th} iteration. |

${P}_{p\_AGA,C\_\mathrm{max}}$ | The maximum of cross probability of AGA under the p_AGA^{th} iteration. |

${f}_{p\_AGA,\mathrm{max}}$ | The maximum of fitness function of AGA under the p_AGA^{th} iteration. |

${f}_{p\_AGA,mean}$ | The mean of fitness function of AGA under the p_AGA^{th} iteration. |

${P}_{p\_AGA,M}$ | The mutation probability of AGA under the p_AGA^{th} iteration. |

${P}_{p\_AGA,M,\mathrm{max}}$ | The maximum of mutation probability of AGA under the p_AGA^{th} iteration. |

${K}_{AGA}$ | The adjustment parameter of fitness function of AGA. |

${h}_{i}$ | The iteration times-related variable of AGA algorithm. |

$T{2}_{p\_AGA}^{\mathrm{max}}$ | The maximum of cost-revenue function under the p_AGA^{th} iteration. |

$p\_AG{A}_{\mathrm{max}}$ | The maximum iteration number of AGA. |

${x}_{ij}$ | The coordinate of flight path. |

${x}_{j}^{\mathrm{min}}$ | The minimum value of x_{ij}. |

${x}_{j}^{\mathrm{max}}$ | The maximum value of x_{ij}. |

$NP$ | The total amount of bee of ABC algorithm. |

$D$ | The parameter dimension of ABC algorithm. |

${f}_{p\_IABC}$ | The fitness function of IABC algorithm. |

$T{1}_{p\_IABC}$ | The cost-revenue function of IABC algorithm under p_IABC^{th} iteration. |

${x}_{best,j}$ | The j^{th} dimension component of global optimal solution of current population. |

$\epsilon (p\_IABC)$ | The balanced searching factor 1 of IABC algorithm. |

$\delta (p\_IABC)$ | The balanced searching factor 2 of IABC algorithm. |

$p\_IABC$ | The current iteration number of IABC algorithm. |

$p\_IAB{C}_{\mathrm{max}}$ | The maximum iteration number of IABC algorithm. |

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**Figure 3.**Sketch map of weather station and its actual remote sensing map. (

**a**) Sketch map of weather station. (

**b**) Actual remote sensing map which comes from Google earth (https://www.google.com/earth/ accessed on 19 January 2020).

**Figure 4.**Sketch map of transmission tower and its simplified model of radio interference distribution. (

**a**) Front and side views of transmission tower. (

**b**) 2D image of bi-GMM. (

**c**) 3D image of bi-GMM.

**Figure 8.**Average minimum and mean fitness function values of GA and AGA when the iteration times are 300, 400, and 500. (

**a**) Statistical evaluation results of fitness function when the iteration times is 300. (

**b**) Statistical evaluation results of fitness function when the iteration times is 400. (

**c**) Statistical evaluation results of fitness function when the iteration times is 500.

**Figure 9.**Examples of path planning and statistical results of fitness function using 300 iterations. (

**a**,

**b**) Path planning examples of ABC and IABC when iteration times is 300. (

**c**) Statistical results of fitness function of ABC and IABC when iteration times is 300.

**Figure 10.**Examples of path planning and statistical results of fitness function using 400 iterations. (

**a**,

**b**) Path planning examples of ABC and IABC when iteration times is 400. (

**c**) Statistical results of fitness function of ABC and IABC when iteration times is 400.

**Figure 11.**Examples of path planning and statistical results of fitness function using 500 iterations. (

**a**,

**b**) Path planning examples of ABC and IABC when iteration times is 500. (

**c**) Statistical results of fitness function of ABC and IABC when iteration times is 500.

**Figure 12.**Results of multi-UAV optimal mission assignment and path planning using different methods. (

**a**) Visualization results of GA+ABC. (

**b**) Visualization results of GA+IABC. (

**c**) Visualization results of AGA+ABC. (

**d**) Visualization results of AGA+IABC.

**Figure 13.**Visualization results of multi-UAV optimal mission assignment and path planning using GA, AGA, PSO, and APFA. (

**a**) Visualization results of GA+PSO. (

**b**) Visualization results of AGA+PSO. (

**c**) Visualization results of GA+APFA. (

**d**) Visualization results of GA+APFA.

**Figure 14.**Visualization simulation examples of proposed method. (

**a**) Global field view of simulation result. (

**b**) Local field view of simulation result.

Representative Algorithm | Algorithm Category | |||

Heuristic Algorithm | Mathematical Programming | Stochastic Intelligent Optimization Method | ||

Mission assignment problem | Tabu search algorithm [13], simulated annealing algorithm [14], genetic algorithm (GA) [15], etc. | Enumeration algorithm [16], dynamic programming [17], etc. | Evolutionary computation [18], swarm intelligence computing [19], artificial immune algorithm [20], etc. | |

Representative Algorithm | Algorithm Category | |||

Mathematical Programming | Artificial Potential Field Method | Graph-Based Method | Intelligent Optimization Method | |

Path planning problem | Dynamic programming [21], nonlinear programming method [22], etc. | Basic artificial potential field method [23], improved artificial potential field method [24], etc. | Dijkstra algorithm [25], A* algorithm [26], Voronoi diagram method [27], probabilistic roadmaps method [28], etc. | Swarm intelligence computing [29], bionic algorithm [30], etc. |

Wind Speed (m/s) | (0.0, 0.2] | (0.2, 7.9] | (7.9, 13.8] | (13.8, 24.4] | (24.4, 100.0] |

Threat Degree | 1 | 2 | 3 | 4 | 5 |

Intensity of Importance | Definition |
---|---|

1 | Equally important |

3 | Weakly important |

5 | Essentially important |

7 | Very strongly important |

9 | Absolutely important |

2, 4, 6, 8 | Importance between the above odd numbers |

Test Experiment 1 | |||

Number of Mission Point | Coordinate of Mission Point | Number of Mission Point | Coordinate of Mission Point |

1 | (50, 70) | 5 | (75, 75) |

2 | (20, 48) | 6 | (90, 30) |

3 | (30, 65) | 7 | (26, 30) |

4 | (60, 80) | 8 | (80, 40) |

Test Experiment 2 | |||

Number of Mission Point | Coordinate of Mission Point | Number of Mission Point | Coordinate of Mission Point |

1 | (50, 70) | 10 | (105, 60) |

2 | (20, 48) | 11 | (98, 49) |

3 | (30, 65) | 12 | (93, 87) |

4 | (60, 80) | 13 | (47, 12) |

5 | (75, 75) | 14 | (84, 17) |

6 | (90, 30) | 15 | (39, 75) |

7 | (26, 30) | 16 | (98, 74) |

8 | (80, 40) | 17 | (75, 24) |

9 | (60, 20) | 18 | (39, 8) |

Fitness Function Value | |||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | ||

Testexperiment 1 | GA | 203.5649 | 322.9047 | 33.6182 | 261.5839 |

AGA | 200.8118 | 286.4434 | 30.7327 | 225.2601 | |

Textexperiment 2 | GA | 506.3372 | 744.7273 | 56.8380 | 623.5432 |

AGA | 369.5323 | 493.2025 | 30.5143 | 429.6063 | |

Processing Time (s) | |||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | ||

Testexperiment 1 | GA | 1.61 | 2.16 | 0.11 | 1.75 |

AGA | 1.92 | 2.75 | 0.24 | 2.49 | |

Textexperiment 2 | GA | 2.1 | 3.1 | 0.26 | 2.59 |

AGA | 3.36 | 4.44 | 0.16 | 3.86 |

Result of Optimal Mission Point Schedule | ||||
---|---|---|---|---|

Iteration Times = 300 | Iteration Times = 400 | Iteration Times = 500 | ||

Testexperiment 1 | GA | 2, 3, 4, 5, 1, 7, 6, 8 | 2, 7, 3, 1, 5, 4, 8, 6 | 7, 3, 2, 1, 4, 5, 8, 6 |

AGA | 7, 2, 3, 1, 4, 5, 8, 6 | 7, 2, 3, 1, 4, 5, 8, 6 | 7, 2, 3, 1, 4, 5, 8,6 | |

Testexperiment 2 | GA | 13, 8, 6, 4, 5, 11, 10, 12, 16, 17, 9, 2, 1, 15, 3, 18, 7, 14 | 14, 9, 13, 2, 1, 11, 10, 16, 17, 18, 7, 15, 3, 4, 5, 12, 8, 6 | 7, 2, 14, 6, 10, 11, 8, 17, 9, 13, 18, 16, 12, 15, 1, 3, 4, 5 |

AGA | 2, 1, 12, 16, 10, 11, 17, 14, 6, 8, 5, 4, 15, 3, 7, 18, 13, 9 | 13, 18, 7, 2, 3, 15, 1, 9, 14, 17, 4, 5, 12, 16, 8, 6, 11, 10 | 3, 15, 1, 17, 9, 2, 7, 18, 13, 14, 6, 8, 11, 5, 4, 12, 16, 10 |

Num | Center Coordinate, Radius, Rain State ^{a}, and Wind Degree of Severe Weather Threat Source | Center Coordinate, (μ1_{i}_{,j, p,1}, σ1^{2}_{i}_{,j,p,1}), (μ2_{i}_{,j,p.2}, σ2^{2}_{i}_{,j,p.2}), w_{j}_{,p,1}, and w_{j}_{,p.2} of Transmission Tower Threat Source | Center Coordinate, Minimum Height, Maximum Height, and Radius of Upland Threat Source |
---|---|---|---|

1 | (31, 21), 10, 0, 4 | (13, 63), (1, 5), (1, 9), 0.5, 0.5 | (38, 48), 150, 300, 13 |

2 | (67, 32), 15, 1, 2 | (60, 75), (2, 6), (2, 10), 0.5, 0.5 | (88, 77), 150, 300, 10 |

3 | (75, 97), 8, 0, 3 | (20, 83), (3, 7), (3,11), 0.5, 0.5 | (70, 60), 150, 300, 6 |

4 | (39, 90), 9, 0, 3 | (92, 57), (4, 8), (4, 12), 0.5, 0.5 | (101, 25), 150, 300, 14 |

^{a}The rain state is: if there is a rain the value will be 1; otherwise the value should be 0.

Iteration Times | Method | Optimal Fitness Function | Path Length | Processing Time |

300 | ABC | 0.8957 | 172.5320 | 3.58 |

IABC | 0.8984 | 167.8581 | 5.76 | |

Iteration Times | Method | Optimal Fitness Function | Path Length | Processing Time |

400 | ABC | 0.8980 | 168.1855 | 4.51 |

IABC | 0.8987 | 167.7283 | 7.42 | |

Iteration Times | Method | Optimal Fitness Function | Path Length | Processing Time |

500 | ABC | 0.8975 | 167.4791 | 5.54 |

IABC | 0.8987 | 167.4733 | 9.03 |

Fitness Function/The Iteration Times Is 300 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 0.8985 | 0.8943 | 1.3 × 10^{−3} | 0.8972 |

IACB | 0.8986 | 0.8967 | 4.6143 × 10^{−4} | 0.8981 |

Path Length/The Iteration Times Is 300 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 167.2298 | 172.5320 | 1.3489 | 168.6910 |

IACB | 164.8105 | 168.5795 | 0.97294 | 167.6903 |

Processing Time (s)/The Iteration Times Is 300 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 3.56 | 4.27 | 0.1541 | 3.95 |

IACB | 5.70 | 6.36 | 0.1322 | 6.02 |

Fitness Function/The Iteration Times Is 400 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 0.8987 | 0.8964 | 5.3594 × 10^{−4} | 0.8982 |

IACB | 0.8988 | 0.8981 | 1.7287 × 10^{−4} | 0.8986 |

Path Length/The Iteration Times is 400 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 166.6625 | 169.4589 | 0.6558 | 168.2398 |

IACB | 166.5989 | 168.4041 | 0.4691 | 167.8869 |

Processing Time (s)/The Iteration Times Is 400 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 5.23 | 4.53 | 0.1462 | 4.70 |

IACB | 7.86 | 7.55 | 0.0778 | 7.68 |

Fitness Function/The Iteration Times Is 500 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 0.8987 | 0.8975 | 2.8031 × 10^{−4} | 0.8985 |

IACB | 0.8988 | 0.8982 | 1.3235 × 10^{−4} | 0.8987 |

Path Length/The Iteration Times is 500 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 167.4791 | 169.0534 | 0.3398 | 168.4406 |

IACB | 167.3409 | 168.5107 | 0.2934 | 168.2355 |

Processing Time (s)/The Iteration Times Is 500 | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

ABC | 5.29 | 6.09 | 0.2080 | 5.60 |

IACB | 8.83 | 10.13 | 0.3193 | 9.41 |

Threat Source | UAV Performance | |
---|---|---|

Threat source | 1 | 7 |

UAV performance | 1/7 | 1 |

$\mathbf{Oil}\text{}\mathbf{Consumption}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{O}}\mathbf{\right)}$ | $\mathbf{Flight}\text{}\mathbf{Distance}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{D}}\mathbf{\right)}$ | |
---|---|---|

Oil consumption (${\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{O}}$) | 1 | 9 |

Flight distance (${\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{D}}$) | 1/9 | 1 |

$\mathbf{Weather}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{W}\mathit{R}}\mathbf{\right)}$ | $\mathbf{Transmission}\text{}\mathbf{Tower}\text{}\left({\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{T}\mathit{T}}\right)$ | $\mathbf{Upland}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{U}\mathit{T}}\mathbf{\right)}$ | |
---|---|---|---|

Weather (${\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{W}\mathit{R}}$) | 1 | 9 | 9 |

Transmission tower (${\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{T}\mathit{T}}$) | 1/9 | 1 | 1 |

Upland (${\mathit{\delta}}_{\mathit{M}\mathit{P}}^{\mathit{U}\mathit{T}}$) | 1/9 | 1 | 1 |

Name | ${\delta}_{MP}^{D}$ | ${\delta}_{MP}^{O}$ | ${\delta}_{MP}^{WR}$ | ${\delta}_{MP}^{TT}$ | ${\delta}_{MP}^{UT}$ |

Value | 0.0125 | 0.1125 | 0.7159 | 0.0795 | 0.0795 |

Threat Source | UAV Performance | |
---|---|---|

Threat source | 1 | 3 |

UAV performance | 1/3 | 1 |

$\mathbf{Oil}\text{}\mathbf{Consumption}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{O}}\mathbf{\right)}$ | Flight Distance (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{D}}$) | |
---|---|---|

Oil consumption (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{O}}$) | 1 | 6 |

Flight distance (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{D}}$) | 1/6 | 1 |

$\mathbf{Weather}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{W}\mathit{R}}\mathbf{\right)}$ | $\mathbf{Transmission}\text{}\mathbf{Tower}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{T}\mathit{T}}\mathbf{\right)}$ | $\mathbf{Upland}\text{}\mathbf{\left(}{\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{U}\mathit{T}}\mathbf{\right)}$ | |
---|---|---|---|

Weather (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{W}\mathit{R}}$) | 1 | 8 | 8 |

Transmission tower (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{T}\mathit{T}}$) | 1/8 | 1 | 2 |

Upland (${\mathit{\delta}}_{\mathit{R}\mathit{P}}^{\mathit{U}\mathit{T}}$) | 1/8 | 1/2 | 1 |

Name | ${\delta}_{RP}^{D}$ | ${\delta}_{RP}^{O}$ | ${\delta}_{RP}^{WR}$ | ${\delta}_{RP}^{TT}$ | ${\delta}_{RP}^{UT}$ |

Value | 0.2143 | 0.0357 | 0.5968 | 0.094 | 0.0592 |

Number of Mission Point | Coordinate of Mission Point | Number of Mission Point | Coordinate of Mission Point | Number of Mission Point | Coordinate of Mission Point |
---|---|---|---|---|---|

1 | (23, 70) | 3 | (44, 72) | 5 | (85, 43) |

2 | (25, 40) | 4 | (51, 38) | 6 | (75, 82) |

**Table 19.**Results of multi-UAV optimal mission assignment and path planning using different optimization methods.

Method Name | Group Assignment Result ^{a} | Mission Assignment Result ^{b} | Total Revenue Result | Total Cost Result | Processing Time (s) | Path Length |
---|---|---|---|---|---|---|

GA+ABC | Group A: 8, 1, 2 Group B: 7, 2, 0 | Group A: 1, 3, 6 Group B: 2, 4, 5 | 79.5684 | 0.1453 | 62.27 | 340.9001 |

GA+IABC | Group A: 7, 2, 0 Group B: 8, 1, 2 | Group A: 2, 4, 5 Group B: 1, 3, 6 | 79.4320 | 0.1633 | 82.44 | 334.9619 |

AGA+ABC | Group A: 7, 2, 0 Group B: 8, 1, 2 | Group A: 2, 4, 5 Group B: 1, 3, 6 | 79.5740 | 0.1435 | 92.62 | 337.5118 |

AGA+IABC | Group A: 7, 2, 0 Group B: 8, 1, 2 | Group A: 2, 4, 5 Group B: 1, 3, 6 | 79.6475 | 0.1326 | 113.68 | 329.1168 |

^{a}The group assignment result means the grouping results of drug delivery, image collection, and communication relay UAVs.

^{b}The Mission assignment result means the flight orders of mission points.

**Table 20.**Statistical results of average revenue, average cost, average processing time, and average path length using different mission assignment and path planning methods.

Average Revenue Result | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+ABC | 79.6017 | 79.1356 | 0.1157 | 79.4761 |

GA+IABC | 79.6265 | 79.3540 | 0.0706 | 79.5123 |

AGA+ABC | 79.5799 | 77.7220 | 0.5315 | 79.3207 |

AGA+IABC | 79.6475 | 79.4919 | 0.0363 | 79.5749 |

Average Cost Result | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+ABC | 0.1418 | 0.1788 | 0.0105 | 0.1534 |

GA+IABC | 0.1350 | 0.1633 | 0.0072 | 0.1461 |

AGA+ABC | 0.1374 | 0.1985 | 0.0174 | 0.1530 |

AGA+IABC | 0.1326 | 0.1489 | 0.0039 | 0.1413 |

Average Processing Time (s) | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+ABC | 61.31 | 69.34 | 2.1148 | 64.52 |

GA+IABC | 79.13 | 86.84 | 2.1571 | 83.54 |

AGA+ABC | 89.92 | 95.73 | 1.9324 | 93.08 |

AGA+IABC | 102.24 | 114.87 | 3.4733 | 108.71 |

Average Path Length | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+ABC | 329.5748 | 340.9091 | 3.7418 | 336.6497 |

GA+IABC | 329.8217 | 343.4356 | 3.4055 | 334.4394 |

AGA+ABC | 331.0667 | 379.0624 | 12.5883 | 339.6279 |

AGA+IABC | 328.6109 | 337.5947 | 2.7720 | 331.9636 |

**Table 21.**Statistical evaluation results of average revenue, average cost, average processing time, and average path length using GA, AGA, PSO, and APFA.

Average Revenue Result | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+PSO | 79.5746 | 77.4224 | 0.7295 | 79.0008 |

AGA+PSO | 79.5918 | 78.0337 | 0.3909 | 79.3464 |

GA+APFA | 79.4929 | 77.5304 | 0.5118 | 79.0061 |

AGA+APFA | 79.5426 | 78.9268 | 0.1757 | 79.3605 |

Average Cost Result | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+PSO | 0.1444 | 0.2815 | 0.0317 | 0.1615 |

AGA+PSO | 0.1411 | 0.1919 | 0.0170 | 0.1533 |

GA+APFA | 0.1445 | 0.1847 | 0.0116 | 0.1601 |

AGA+APFA | 0.1419 | 0.1721 | 0.0083 | 0.1508 |

Average Processing Time (s) | ||||

Best Value | Worst Value | Standard Deviation Value | Mean Value | |

GA+PSO | 112.47 | 120.24 | 115.82 | 2.8234 |

AGA+PSO | 178.92 | 188.56 | 185.02 | 1.8648 |

GA+APFA | 1694.52 | 1798.42 | 30.5664 | 1740.98 |

AGA+APFA | 1802.07 | 1892.88 | 25.0210 | 1855.64 |

Average Path Length | ||||

Best Value | Worst Value | Standard deviation Value | Mean Value | |

GA+PSO | 329.8403 | 397.2150 | 19.3590 | 352.9970 |

AGA+PSO | 330.4529 | 344.4585 | 14.9107 | 350.3686 |

GA+APFA | 364.3596 | 432.0467 | 16.3501 | 379.0128 |

AGA+APFA | 358.4359 | 379.2276 | 6.5640 | 367.8603 |

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## Share and Cite

**MDPI and ACS Style**

Liu, H.; Ge, J.; Wang, Y.; Li, J.; Ding, K.; Zhang, Z.; Guo, Z.; Li, W.; Lan, J.
Multi-UAV Optimal Mission Assignment and Path Planning for Disaster Rescue Using Adaptive Genetic Algorithm and Improved Artificial Bee Colony Method. *Actuators* **2022**, *11*, 4.
https://doi.org/10.3390/act11010004

**AMA Style**

Liu H, Ge J, Wang Y, Li J, Ding K, Zhang Z, Guo Z, Li W, Lan J.
Multi-UAV Optimal Mission Assignment and Path Planning for Disaster Rescue Using Adaptive Genetic Algorithm and Improved Artificial Bee Colony Method. *Actuators*. 2022; 11(1):4.
https://doi.org/10.3390/act11010004

**Chicago/Turabian Style**

Liu, Haoting, Jianyue Ge, Yuan Wang, Jiacheng Li, Kai Ding, Zhiqiang Zhang, Zhenhui Guo, Wei Li, and Jinhui Lan.
2022. "Multi-UAV Optimal Mission Assignment and Path Planning for Disaster Rescue Using Adaptive Genetic Algorithm and Improved Artificial Bee Colony Method" *Actuators* 11, no. 1: 4.
https://doi.org/10.3390/act11010004